Mineral resource models are the result of several dozens of parameters, chosen by field technicians, laboratories and resource geologists, but their respective effects and ultimate impact on models are not often captured. Analysing the sensitivity of such a large number of parameters requires automating complex workflows with a specific strategy to avoid expensive computations. The outcome of such analysis allows one to better understand the influence of these parameters, carry out uncertainty analysis studies on selected key parameters and quantify the impact of their variations on the modelled outputs. Uncertainty analysis may be performed through Design of Experiments (DoE) in order to decrease the required computation time compared to a traditional full factorial approach. In traditional DoE, a response surface is modelled using at least square polynomial regression, which does not fully represent nonlinear relationships between parameters. This response surface, regarded as a proxy for the mineral resource modelling workflow, is used to quickly estimate model outputs, typically through Monte Carlo simulations. As response surfaces are purely mathematical regressions, machine learning models are typically good candidates to improve capturing the nonlinear relationships between parameters. By providing response surface models that integrate the nonlinear relationship between parameters, the confidence in the resulting uncertainties would therefore increase. In this paper, we propose to explore a selection of suitable machine learning algorithms, evaluate their ability to generalise from a small training dataset and validate the approach by comparing the difference between the quantifiable space of uncertainty of a case study dataset using the traditional approach, and the modified approach enhanced by machine learning. The objectives of this study are to:–Compare the approach of using different machine learning techniques in the uncertainty analysis methodology versus the traditional approach (Response Surface Model using a quadratic polynomial regression). –Understand whether these machine learning models can generalise from a small dataset, meaning can they learn outside of the training values. –Find out whether the Box-Behnken design is suitable for machine learning. First findings for this case study suggest selected machine learning models show similar results than traditional response surface modelling using a quadratic fit. To ensure that the quadratic fit is not bound to the Box-Behnken design, full factorial and random samplings were also performed and confirm the quadratic nature of the studied output. In order to validate these findings, additional studies on output known to be of higher order need to be performed. Selected machine learning models yield different results depending on the DoE used for training. While the Box-Behnken design does not seem appropriate as a training dataset due to the low variability of the input parameter, the full-factorial design provides much better training data but has the disadvantage of being too computational expensive. Other designs should be investigated to find a good support for training the ML-generated response surface. It is also to note that Machine learning models display different results to each other, suggesting some may be better suited than others in the case of response surface modelling. Typically, our research shows that some algorithms such as Gradient Boosting or Random Forest will overfit the data in this case study.

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Improvement of Uncertainty Quantification of Mineral Resource Estimation Using Machine Learning

  • Hadrien Meyer,
  • Claude Cavelius,
  • Johann Dangin,
  • Gustavo Pilger,
  • Claver Gnamien,
  • Anouar Lachgur

摘要

Mineral resource models are the result of several dozens of parameters, chosen by field technicians, laboratories and resource geologists, but their respective effects and ultimate impact on models are not often captured. Analysing the sensitivity of such a large number of parameters requires automating complex workflows with a specific strategy to avoid expensive computations. The outcome of such analysis allows one to better understand the influence of these parameters, carry out uncertainty analysis studies on selected key parameters and quantify the impact of their variations on the modelled outputs. Uncertainty analysis may be performed through Design of Experiments (DoE) in order to decrease the required computation time compared to a traditional full factorial approach. In traditional DoE, a response surface is modelled using at least square polynomial regression, which does not fully represent nonlinear relationships between parameters. This response surface, regarded as a proxy for the mineral resource modelling workflow, is used to quickly estimate model outputs, typically through Monte Carlo simulations. As response surfaces are purely mathematical regressions, machine learning models are typically good candidates to improve capturing the nonlinear relationships between parameters. By providing response surface models that integrate the nonlinear relationship between parameters, the confidence in the resulting uncertainties would therefore increase. In this paper, we propose to explore a selection of suitable machine learning algorithms, evaluate their ability to generalise from a small training dataset and validate the approach by comparing the difference between the quantifiable space of uncertainty of a case study dataset using the traditional approach, and the modified approach enhanced by machine learning. The objectives of this study are to:–Compare the approach of using different machine learning techniques in the uncertainty analysis methodology versus the traditional approach (Response Surface Model using a quadratic polynomial regression). –Understand whether these machine learning models can generalise from a small dataset, meaning can they learn outside of the training values. –Find out whether the Box-Behnken design is suitable for machine learning. First findings for this case study suggest selected machine learning models show similar results than traditional response surface modelling using a quadratic fit. To ensure that the quadratic fit is not bound to the Box-Behnken design, full factorial and random samplings were also performed and confirm the quadratic nature of the studied output. In order to validate these findings, additional studies on output known to be of higher order need to be performed. Selected machine learning models yield different results depending on the DoE used for training. While the Box-Behnken design does not seem appropriate as a training dataset due to the low variability of the input parameter, the full-factorial design provides much better training data but has the disadvantage of being too computational expensive. Other designs should be investigated to find a good support for training the ML-generated response surface. It is also to note that Machine learning models display different results to each other, suggesting some may be better suited than others in the case of response surface modelling. Typically, our research shows that some algorithms such as Gradient Boosting or Random Forest will overfit the data in this case study.